24 Horsepower, the Facts

Cover for Horsepower, the Facts

Power is a technical term. It does more than sells cars and, in fact, can aid in winning races. Unfortunately its true nature is sometimes poorly understood, even by car enthusiasts. Power is also often put in an unnecessary rivalry with another engine output metric - maximum torque.

There are a lot of explanations on the Internet and elsewhere that try to explain what's what. Some of them are right, some not. Many aren't very clear. What is clear, is the physics behind cars, and I hope that, by providing an explanation based in physics, I can clear up misunderstandings that anyone might have on what horsepower is and what it really says about a car or engine.

In physics, power is the rate of change of energy. A car in motion has a particular kind of energy known as kinetic energy (KE). KE is related to motion, the faster something goes, the more KE it has. The exact relation is KE = .5 * mass * velocity2.
Velocity is something that most people understand, and it's something that a driver wants to maximize when racing. Using the equation above, it's possible to determine the amount of KE carried by a car at a certain speed if we know its mass.

A 1000 kg car traveling at 50 m/s possesses 1,250,000 joules of energy. Note that units are important. Mass is in kilograms (kg), you can't use Newtons or pound-force (as they are weight) unless you use their mass equivalents - the Newton-mass and pound-mass, as long as you include the proper correction factor.

The KE is important and can provide a lot of information. When a car tries to stop, the brakes need to remove all the KE from the car by converting it into heat. The more KE, the more the brakes have to work. It's pretty clear that having a lighter car is better for your brakes. But none of this has to do with horsepower...

Let's imagine the same 1000 kg car from before traveling at 50 m/s as it starts to accelerate. It would be useful to calculate how fast it can accelerate. This can be determined from torque if the gear ratios and tire sizes are known, but goog-ling this information might take minutes!

Instead of using torque, it's possible to use power, and this makes things much easier. Now the gearing and the wheels don't matter at all. Power provides a method to determine the acceleration of a car, whether it has mile wide gear spacing and bicycle tires, or a gear limited speed of 5 mph and monster truck tires.

For simplicity's sake, assume that the engine makes a constant 500,000 Watts (units are important) of power at every RPM. The engine will simply add 500,000 joules of energy to the car every second since a Watt is equivalent to a joule per second.

So the car starts at 1,250,000 Joules or 50 m/s. One second later it will have 1,750,000 joules and its speed will be 59 m/s. At 2 seconds from starting, KE is 2,250,000 and speed is 67 m/s. It's clear that even though power is constant, the acceleration is not. 500,000 W averaged 9 m/s2 acceleration from time zero to one, but only 8 m/s2 from time one to two. This is because 500,000 joules becomes a smaller and smaller percentage of the total KE. The faster the car goes, the harder it is to make it accelerate.

Thinking in terms of energy might seem a little abstract however. Force is a more familiar term, and fortunately, power and force are related. To see this relationship, requires a deeper understanding on energy.

Energy, in general, is the ability to do Work, and Work is force exerted over a distance. 1 Newton of force exerted for 1 meter of distance is 1 joule of work, or 1 joule of energy. Power is the rate of change of energy. For those familiar with calculus, {Power is the derivative of energy. Don't worry, I won't mention calculus again...

Displacement (Distance), Velocity, and Acceleration are related in the same way that energy and power are. Acceleration is the rate of change of velocity, which is the rate of change of distance. Going back to the Work/Force relationship (Energy = Work = Force * Distance), let's turn energy into power by using rate of change (RoC).

  • Power = RoC of Energy
  • Power = RoC of Force * Distance
  • Velocity = RoC of Distance
  • RoC of Force * Distance = Force * RoC of Distance
  • RoC of Force * Distance = Force * Velocity
  • Power = Force * Velocity

Now if the engine's power is known, so is the force pushing the car. Force and Acceleration are already known.

  • F = ma
  • Acceleration = Force / mass
  • Acceleration = Power /(Velocity * mass)

Unlike the KE method used before, this new equation can calculate the acceleration at any point in time. Going back to the example car at 1000 kg with the 500,000 W engine, acceleration is 10 m/s2 at time zero, 8.5 m/s2 at time one, and 7.5 m/s2 at time two.

Horsepower tells you everything you need to know about how the car will accelerate. Power and torque are really the same thing as far as the car in concerned, but horsepower is far easier to use, and this is why it is such a popular metric.

The power and force relationship also allows for other helpful calculations, like those involving drag. Drag is a force, but using the equation relating power to force, it's possible to convert drag force into drag power.

Drag power can be thought of as the opposite of an engine. Instead of creating power, it absorbs it and slows the car down. To see the effect of drag on a car's acceleration, add the drag power to the engine power. Remember that drag power will be negative in this case. Since drag gets bigger with speed, at some point the engine power + drag power will equal zero. At that point, the car would be at its maximum speed.

All of this still leaves one question, where did the horsepower vs torque argument come from? It's actually a result of poor terminology. The heart of the argument lies with the engine's power-band, and not the peak values of horsepower and torque or the individual properties of those two quantities.

Peak refers to the maximum values of power and torque. These numbers can be misleading because they only occur in a narrow RPM range. As long as an engine does not have continuously variable transmission (CVT) with no distinct gear ratios, the power and torque over a range of RPM is more important than the peak values.

For example, a 500 hp car can easily be quicker than a 1000 hp car. If the 500 hp car produces at least 90% of peak power within 2000 RPM of the peak power RPM, it will easily outrun the 1000 hp car that only produces 125 hp of power.

Going back to the horsepower vs torque debate, a torque-rich engine is one that produces torque over a wide range of RPM, or one that produces large amount of torque (and thus horsepower) at low RPM. This gives the car good acceleration from a low speed even if the engine is not spinning very fast. This is great for road cars where the RPM is usually low and there is a lot of stop and go driving.

Conversely, a horsepower-rich engine is one that forgoes torque at low RPM in order to produce more torque (and thus horsepower) at high RPM. This is actually preferred for race cars, and the reason should be obvious once the relationship between power and torque is understood. Power is proportional to torque multiplied by RPM. In other words, 500 units of torque produces more power at 6000 RPM than it does at 5000 RPM. The "horsepower" engine produces more power overall, and this makes it faster.

This isn't to say that low end torque isn't important for race cars though. Depending on the track, a wide, torque-rich power-band can prove advantageous. A torque-ish engine requires less downshifting then a peaky engine, and it also allows the gears to be spaced further apart or for unneeded gears to be dropped completely to save weight.

In the end, power isn't all that complicated and it's not some superfluous number. It's a very helpful performance metric and should be seriously considered in any comparison between sports cars.

13y ago by FastestLaps
User avatar
User avatar

Shaggy  12y ago

Great explanation, that explains a lot and helps me to understand horsepower and torque better, and explains why a vehicle with an engine with more horsepower than torque has a high top speed while a vehicle with more torque than horsepower, better low end acceleration, and a vehicle with equal horsepower and torque has the best of both worlds, fascinating.


User avatar

Matt  13y ago

This is the way I understand it and I am not an engineer:
Torque is how big my bucket is, power is how big my tap is!
AVERAGE power determines acceleration. This is determined by gearing and the power curve. One powertrain is not superior to the other unless we know the gearing and weight difference.
I believe NA engines are legislated to be used in racing because they have the best throttle control. This gives a driver the most control and is therefore the safest option.


User avatar

Anon  13y ago

Good article. I am waiting to new era of hybrid performance. An non-compromised high-end power engine coupled with electric motor to give low-end push can give both performance and fuel-efficiency. If only battery technology could give us light sources of electricity.


User avatar

Viking  13y ago

I agree, a very good article. Of course quoted horsepower at the crank/flywheel is modified by drive train losses before reaching the drive wheels. Chassis dynos (Dynojet, and others) measure power at the wheels, and can give useful insight on how a car will perform (if, and only if the operators take into account all the test conditions). Looking at Dynojet results, and comparing the numbers with the factory quoted horsepower, it is clear that some transmission/drive trains are more efficient at putting the power to the wheels. Normal torque converter automatics lose more power than manuals and auto clutch transmissions. Even manual transmission models have differences in efficiency it seems. Based on factory horsepower versus Dynojet chassis dyno figures the loss ranges from 8% to 19% for modern manual transmission cars.


User avatar

ramzi  13y ago

GOOD article, so guys just keep in mind , power is torque multiplied by rpm, thus when torque is higher,power is also higher for a given rpm.also keep in mind that at high rpms,torque might be decreasing however power is rising beacuse the rise in rpms is more than decline in torque :-)


User avatar

E  13y ago

I found this a bit confusing. How is the 1000hp car only producing 125 horsepower? Are you talking about at a certain RPM range? I must say that would be a heck of a design failure lol.

Yes a typo there, it would produce 125 hp off the peak RPM, which would mean that although the engine would technically be a 1000 hp engine, it would act like a 125 hp engine.

And calling it a design failure would be an insult to design failures lol


User avatar

G  13y ago

I imagine some of the confusion has arisen from the fact that engines with the highest torque output also have their peak torque figure lower down the rev range than equivalent engines, leading people to erroneously conclude that it is the amount of torque - not where the torque peaks and its subsequent effect on the power curve - that is responsible for the 'low down grunt', which is a favourite claim of diesel proponents. Ironically, it is the low output of NA diesels and the dependency on turbocharging that gives diesels there broader power curve, as is true of all engines that depend on turbocharging to produce power. All this said and done however, it would seem that the trend of transmission technology - particularly the current 8 speed autos - will soon make power curves irrelevant, given that current autos already do a very good job of keeping engines operating within their powerbands.


User avatar

FastestLaps  13y ago

@Apathy

Your HP article is in the pipeline. I don't want two horsepower articles back to back :D


User avatar

monkeypop  13y ago

"A Torque peak higher up in the rev range means more HP. A torque curve tuned to be in the high RPM range will give you an engine which is optimised for max HP. Cars tuned for low end tend to sacrifice the high end HP. HP is what will determine how quickly you can add energy (ie speed) to your car."

What you are saying does not relate at all to what I said. I am talking about a car with both a flat torque curve and a flat/sloping power curve, not a car tuned just for low end torque.

Horsepower is what it is. If a car has both great horsepower on a gentle slope and a flat torque curve then you cant very well say it doesnt have optimum power just because it produces good low end torque or that a engine tuned for high end torque is capable of doing more work.


User avatar

monkeypop  13y ago

"That's why we have gears.

erhaps an automatic would suit you. A 150hp 2L car in the right gear will out accelerate your ZO6 doing 1300rpm (the ZO6 putting out < 100Hp at that rpm) and he will get better milleage too!"

Indeed cars have gears, and the large majority of cars will bog down and stall if you shift from first to 4th at low RPM.

No, automatics are awful.

"Thats fine, but id use the car for the performance personally. If your bothered about your MPG you should be driving a nice 1.6l that will return you 60+mpg. This is fastest laps after all."

I did use it for the performance but I did not drive 100% of the time like I was on a race track. I drove the car on the street, hence it was nice to get good mileage. This is a article about power/torque and their curves.. hence that is what I am talking about.


User avatar

BR2,  13y ago

This article is too long for me to take interest in-_-


User avatar

bengismo  13y ago

"Most engines will bog down and shutter if trying to accelerate from top gear at low speeds."
That's why we have gears.

erhaps an automatic would suit you. A 150hp 2L car in the right gear will out accelerate your ZO6 doing 1300rpm (the ZO6 putting out < 100Hp at that rpm) and he will get better milleage too!

"How exactly would a engine be able to do more work with a torque curve in the upper RPM range than a torque curve that is flat and provides torque at any RPM? "

A Torque peak higher up in the rev range means more HP. A torque curve tuned to be in the high RPM range will give you an engine which is optimised for max HP. Cars tuned for low end tend to sacrifice the high end HP. HP is what will determine how quickly you can add energy (ie speed) to your car. As per the article. Track Race cars have engines tuned for high end torque with no real need for low end. Ie Maximum performance.

"There are not many cars out there with the performance of a corvette that can attain the MPG rating. "
Thats fine, but id use the car for the performance personally. If your bothered about your MPG you should be driving a nice 1.6l that will return you 60+mpg. This is fastest laps after all.


User avatar

monkeypop  13y ago

"I guess its a personal choice as to where a person wants their torque.

Me personally, higher, in the rev range is what I want as the car can literally do more work regardless of gearing."

I dont really follow? How exactly would a engine be able to do more work with a torque curve in the upper RPM range than a torque curve that is flat and provides torque at any RPM?

I just dont follow the logic. It would seem better to have torque at any RPM so you are getting a good torque/power output at any rev range vs having it limited to lower or upper rev range.


User avatar

monkeypop  13y ago

"Yes, I agree that prolonged high rpms aren't wanted for economy but in any car you can use a higher gear if you wanted, it would just take longer to accelerate"

Actually that is not the case. Most engines will bog down and shutter if trying to accelerate from top gear at low speeds.

"Corvette use a 6.3L engine to produce 436 HP. I would want more from that displacement since other manufacturers can beat that HP with 4.4L of displacement (NA) and even more with turbo cars."

Ahh, and back to the argument of displacement. You cannot compare displacement of OHV vs OHC. While that corvette engine may have larger displacement they are typically smaller in size and weight than OHC engines of the same displacement.

There are not many cars out there with the performance of a corvette that can attain the MPG rating.

Of course I did not buy the vette for economy but I dont go around driving like a mad man most of the time so why not get better gas mileage when driving normally? Corvettes are able to get far greater mileage than their EPA ratings because of the flat torque curve.
They even have a feature that requires you to shift directly from 1st to 4th when operating at low RPM to save fuel. This goes against your claim that "changing gears does not effect mileage". The large majority of engines could not go from 1st to 4th at low RPM without bogging down or stalling.


User avatar

Ferrari driver  13y ago

you are alright.
:) :)


User avatar

bengismo  13y ago

(it cut of my post - character limit)

Anyway, typically rally drivers will want low end torque for pulling out of slow corners, track cars will normally want a high end toque to maximise HP.

I guess its a personal choice as to where a person wants their torque.

Me personally, higher, in the rev range is what I want as the car can literally do more work regardless of gearing.
:)


User avatar

bengismo  13y ago

This may be going off topic really as this is "fastest laps" not "most efficient laps"

Your talking about efficiency and an engine with good low end torque is not necessarily more efficient then any other engine. It takes the same amount of energy to accelerate the car from 30 to 60mph regardless of what gear you use to do it - the article explains that. How far down the throttle is pressed is what controls how much fuel is thrown into the engine. Yes, I agree that prolonged high rpms aren't wanted for economy but in any car you can use a higher gear if you wanted, it would just take longer to accelerate.

A car producing more power/torque at lower rpm will often simply be using more fuel to do so. You only get the good fuel economy while cruising at a constant speed. The energy you use to accelerate is taken from fuel after all.

Besides, the article was about horsepower and torque. Not engine cruising efficiency. That is shown in MPG figures not in HP or torque figures/curves.

Im sure you didnt buy the corvette to get fuel economy did you? lol

Corvette use a 6.3L engine to produce 436 HP. I would want more from that displacement since other manufacturers can beat that HP with 4.4L of displacement (NA) and even more with turbo cars. There are much more fuel efficient cars out there too. What it does give you is lots of nice low end torque though which is obviously what you like.

Look at the maths equation below, perfectly flat torque curves and flat


User avatar

monkeypop  13y ago

"Having to change gear doesnt affect fuel economy. Putting you foot down does."

If you are driving and someone in front of you slows down to turn and you have the low end torque to stay in top gear rather than down shift when you re-accelerate it most certainly does effect fuel economy. Constantly running through the RPM rather than staying in top gear at a more steady lower RPM burns more fuel.

"If you care about fuel economy then you shouldnt really be bothered about the power you producing."

It is nice to have both. My corvette got over 30mpg if I was just cruising but still had the performance when I needed it.

"Since hp and torque are linked you cant have a flat hp curve and a flat torque at the same time."

OHV engines typically produce nice flat torque curves and power curves compared to the very steep curves of OHC engines. Now this isnt always the case, I'm just saying in general.


User avatar

bengismo  13y ago

Since hp and torque are linked you cant have a flat hp curve and a flat torque at the same time.

Typically you have flat torque curve engines (Eg M3) which give a peaky horsepower curve at the top end or you have flat power curve engines (Eg Scooby 300Hp engine) which have a peak low torque.

No engine exists that has flat curve for both.

Having to change gear doesnt affect fuel economy. Putting you foot down does.

If you care about fuel economy then you shouldnt really be bothered about the power you producing.


User avatar

monkeypop  13y ago

"A nice load of torque low down in the rev range feels nice but its for lazy drivers who dont want to have to change down a gear. Torque at low RPM doesn't make much power."

Well they do have certain advantages. Its not just being lazy and not wanting to shift but not having to shift results in better fuel economy.

And what if a engine produces a nice flat torque curve and power curve? Would that not be superior to a engine with a steep torque/power curve since it makes good power at any RPM?